灰色系统理论的多目标可靠性稳健设计

通过对目标函数和约束条件进行灵敏度分析，生成目标函数和约束函数的灵敏度附加项，提出了2种基于灵敏度附加目标函数的可靠性稳健优化设计模型；针对不同评价者对目标获取信息的局限性，基于灰色系统理论把评价者对目标的评估分配在一定范围内，给出了计算各目标函数权重系数的专家评估方法. 应用Matlab7.1语言的优化工具箱和符号工具箱实现圆柱螺旋压缩弹簧的多目标可靠性稳健优化设计. 算例表明，该方法具有较高的精度和可靠度，为机械零件的可靠性设计提供了理论依据.

Multi-Objective Robust Design for Reliability Based on Grey System Theory

Additional items of sensitivity of objective and constraint functions are generated through analyzing the corresponding functions objective functions and constraints. Two models of optimization design for reliability are proposed based on the additional items of sensitivity. According to the limitations of information for objective functions obtained from different evaluators, the objective functions and the evaluators' assessment based on gray system theory was allocated in a certain range. The expert assessment method is presented to calculate the weight coefficients of the objective functions. Reliability-based robust optimization design of cylindrical helix spring is achieved by using the optimization toolbox and symbolic toolbox of Matlab. Numerical examples prove that the proposed approach which provided the theoretic basis for the reliability design of the mechanical elements has a higher precision and reliability.